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Determine the fourth roots of -16
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In the complex plane, -16 = .
The modulus of -16 is , the argument is .
Therefore, according to the general theory, the fourth roots of -16 are four complex numbers
1) = = ;
2) = = = ;
3) = = = ;
4) = = = .
Answer. The four values of fourth root of -16 are , , and .
For this "general theory" see the lesson
- How to take a root of a complex number
in this site.
There is a bunch of my lessons on complex numbers
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Raising a complex number to an integer power
- How to take a root of a complex number
- Solution of the quadratic equation with real coefficients on complex domain
- How to take a square root of a complex number
- Solution of the quadratic equation with complex coefficients on complex domain
in this site.